Percentage formulas
| Question | Formula | Example |
|---|---|---|
| What is P% of X? | P ÷ 100 × X | 18% of 245 = 44.1 |
| X is what % of Y? | X ÷ Y × 100 | 15 of 60 = 25% |
| Percent change from A to B | (B − A) ÷ |A| × 100 | 50 → 65 = +30% |
| X is P% of what? | X ÷ (P ÷ 100) | 30 is 20% of 150 |
| Percentage difference | |A − B| ÷ ((A + B) ÷ 2) × 100 | 40 and 50 = 22.22% |
Percent change vs percentage difference vs percentage points
Percent change compares a new value to an old one, so direction matters: going from 50 to 65 is +30%, but going from 65 to 50 is −23.08%. Percentage difference compares two values with no "before" and "after", so it uses their average and is the same both ways. Percentage points describe the gap between two percentages: an interest rate rising from 4% to 5% is up 1 percentage point, which is a 25% increase.
Negative numbers
When the starting value is negative, Calcist divides by its size (absolute value), which is the usual convention in finance. So a change from −10 to 5 shows as a 150% increase: it rose by 15, which is 1.5 times the starting size of 10. Some textbooks divide by −10 instead and get −150%, which reads as a decrease even though the number went up. If the starting value is 0, there's no percent change at all, because any rise from zero is infinitely large in percent terms.
Quick tricks
- 10%: move the decimal point one place left. 10% of 245 is 24.5.
- Percentages swap: 18% of 50 is the same as 50% of 18, which is 9.
- Increase by a percent: multiply by 1 plus the percent. Adding 8% tax to $40 is 40 × 1.08 = $43.20.
- Ups and downs don't cancel. A 20% rise followed by a 20% fall leaves you 4% lower (1.2 × 0.8 = 0.96).
You can also type questions like 18% of 245 or 15 is what percent of 60 straight into the calculator on the home page.